Prime Distance

Number theory studies the properties of integers, and among them prime numbers have fascinated mathematicians for thousands of years. A prime is an integer greater than $1$ that has no proper divisors: it is divisible only by $1$ and by itself. The smallest primes are $2, 3, 5, 7$, and primes grow steadily sparser as numbers get larger.

Two primes are called adjacent when both are prime and there is no other prime strictly between them. For example, $2$ and $3$ are adjacent primes.

You are given two integers $L$ and $U$ with $1 \le L < U \le 2{,}147{,}483{,}647$. Within the range $[L, U]$ you must find:

• the closest pair of adjacent primes $C_1 < C_2$, i.e. the pair that minimizes $C_2 - C_1$;
• the most distant pair of adjacent primes $D_1 < D_2$, i.e. the pair that maximizes $D_2 - D_1$.

If several pairs achieve the same distance, choose the one that appears first (the pair with the smallest first element).

Input consists of several lines and continues until end of file. Each line contains two positive integers $L$ and $U$ separated by a space, with $L < U$. On any single line the difference $U - L$ does not exceed $1{,}000{,}000$.

For each input line print one line.

• If $[L, U]$ contains fewer than two primes, so that no pair of adjacent primes exists, print:

  There are no adjacent primes.

• Otherwise print the closest and the most distant pairs in the form:

  C1,C2 are closest, D1,D2 are most distant.

  where C1,C2 is the closest pair of adjacent primes and D1,D2 is the most distant pair, the two numbers of each pair separated by a comma.